Gluing n-tilting and n-cotilting subcategories

Abstract

Recently, Wang, Wei and Zhang define the recollement of extriangulated categories, which is a generalization of both recollement of abelian categories and recollement of triangulated categories. For a recollement $(\mathcal{A},\mathcal{B},\mathcal{C})$ of extriangulated categories, we show that $n$-tilting (resp. $n$-cotilting) subcategories in $\mathcal{A}$ and $\mathcal{C}$ can be glued to get $n$-tilting (resp. $n$-cotilting) subcategories in $\mathcal{B}$ under certain conditions.

arXiv comment12 pages